FWinFormer: A Frequency-Domain Deep Learning Framework for 3D Ocean Subsurface Temperature Prediction

Subsurface temperature is an important parameter for characterizing oceanic physical processes, and accurate prediction of subsurface temperature is essential for understanding oceanic changes. Existing methods primarily focus on spatial modeling but offer limited characterization of the spatiotemporal structure and frequency features of sea temperature. They also suffer from restricted receptive fields and limited ability to model long-term dependencies. In this study, we propose a deep learning model named Fourier Window Transformer (FWinFormer), which integrates frequency-domain modeling to predict the three-dimensional subsurface temperature over the next 24 days. The model incorporates both temporal and frequency characteristics to enhance prediction accuracy. It consists of three modules: a Spatial Block Encoder, a Translator, and a Spatial Block Decoder. The spatial encoding and decoding modules are designed to extract spatial features, while the Translator models multi-scale temporal features based on the features extracted by the encoding and decoding modules. The input consists of 24 days of historical satellite observations, including sea-surface temperature (SST), salinity (SSS), eastward velocity (SSU), northward velocity (SSV) and height (SSH). We compared the model predictions with reanalysis data and evaluated performance from the perspectives of temporal evolution, spatial distribution, and vertical structure. Additionally, we validated the predicted temperatures against in situ observations. The results show that the model achieves strong and consistent performance across various temporal scales and spatial regions, with MAE, RMSE, and R2 values of 0.529, 0.785, and 0.994, respectively, for the 24-day average prediction.